Self-adaptive control method, controller and system for quadrature error compensation

Abstract

The invention is suitable for the technical field of quadrature error compensation of a triaxial MEMS (Micro Electro Mechanical System) gyroscope, and provides a self-adaptive control method, a controller and a system for quadrature error compensation. The method comprises the following steps: acquiring coupling damping and coupling rigidity of the triaxial MEMS gyroscope; forming a dimensionless motion model of the three-axis MEMS gyroscope based on the coupling damping and the coupling rigidity of the three-axis MEMS gyroscope; based on the dimensionless motion model of the three-axis MEMS gyroscope, determining a sliding condition of self-adaptive sliding mode control of the three-axis MEMS gyroscope; and controlling the three-axis MEMS gyroscope based on the sliding condition of the self-adaptive sliding mode control. According to the method disclosed by the invention, the influence of external interference or parameter change on the output precision of the gyroscope is solved, the orthogonal error of the triaxial MEMS gyroscope is effectively compensated, and the output precision of the triaxial MEMS gyroscope is improved.

Description

Technical Field

[0001] The present application belongs to the technical field of orthogonal error compensation for three-axis MEMS gyroscopes, and in particular, relates to an adaptive control method, controller and system for orthogonal error compensation. Background Art

[0002] MEMS gyroscopes have broad market prospects in the fields of navigation and automobiles due to their advantages such as low cost, easy mass production, small size and low power consumption.

[0003] The three-axis MEMS gyroscope is relatively difficult to design and manufacture because it needs to process angular velocity information in three directions at the same time, but this also makes it possible to have better performance in terms of accuracy and stability. Of course, the specific performance also depends on factors such as the manufacturing process, calibration accuracy, and subsequent data processing algorithm of the gyroscope. The orthogonal error caused by the inevitable processing error in the manufacturing process is an important factor affecting the accuracy of the three-axis MEMS gyroscope.

[0004] Therefore, how to solve the influence of external interference or parameter changes on the output accuracy of the gyroscope through control algorithms and perform orthogonal error compensation for the three-axis MEMS gyroscope needs to be solved urgently. Summary of the invention

[0005] To overcome the problems existing in the related art, the embodiments of the present application provide an adaptive control method, controller and system for orthogonal error compensation, which can solve the influence of external interference or parameter changes on the output accuracy of the gyroscope and realize orthogonal error compensation of the three-axis MEMS gyroscope.

[0006] This application is implemented through the following technical solutions:

[0007] In a first aspect, an embodiment of the present application provides an adaptive control method for orthogonal error compensation, which is applied to a three-axis MEMS gyroscope. The method includes:

[0008] Obtain the coupling damping and coupling stiffness of the three-axis MEMS gyroscope;

[0009] Based on the coupling damping and coupling stiffness of the three-axis MEMS gyroscope, a dimensionless motion model of the three-axis MEMS gyroscope is formed;

[0010] Based on the dimensionless motion model of the three-axis MEMS gyroscope, the sliding conditions of the adaptive sliding film control of the three-axis MEMS gyroscope are determined;

[0011] The three-axis MEMS gyroscope is controlled based on the sliding condition of the adaptive sliding film control.

[0012] In a possible implementation manner of the first aspect, a dimensionless motion model of the three-axis MEMS gyroscope is formed based on the coupling damping and coupling stiffness of the three-axis MEMS gyroscope, including:

[0013] The coupling damping and coupling stiffness of the three-axis MEMS gyroscope are used to form an initial motion model of the three-axis MEMS gyroscope; the coupling damping and coupling stiffness reflect the influence of the orthogonal error;

[0014] The initial motion model of the three-axis MEMS gyroscope is dimensionlessly processed to obtain the dimensionless motion model of the three-axis MEMS gyroscope.

[0015] In a possible implementation manner of the first aspect, the dimensionless motion model of the three-axis MEMS gyroscope is expressed as:

[0016]

[0017] in, is the first-order derivative of the dimensionless displacement matrix q in the x, y, and z axes, is the second-order derivative of the dimensionless displacement matrix q in the x, y, z axes; D is the dimensionless damping matrix; the elements of the dimensionless damping matrix include equivalent damping and coupling damping; K is the dimensionless stiffness matrix; the elements of the dimensionless stiffness matrix include equivalent stiffness and coupling stiffness; u is the dimensionless control force matrix in the x, y, z axes; Ω is the dimensionless angular velocity matrix.

[0018] In a possible implementation of the first aspect, determining a sliding condition of an adaptive sliding film control of the three-axis MEMS gyroscope based on a dimensionless motion model of the three-axis MEMS gyroscope includes:

[0019] Obtain the uncertainty factors of the dimensionless motion model of the three-axis MEMS gyroscope;

[0020] Based on the uncertainty factors, the dynamic motion model of the three-axis MEMS gyroscope is determined;

[0021] Determine the Lyapunov function based on the expected trajectory tracking error and parameter estimation error of the dynamic motion model of the three-axis MEMS gyroscope;

[0022] Based on the Lyapunov function, the adaptive law of the adaptive sliding film control of the three-axis MEMS gyroscope is determined;

[0023] Based on the adaptive law of the adaptive sliding film control of the three-axis MEMS gyroscope, the sliding condition of the adaptive sliding film control of the three-axis MEMS gyroscope is determined.

[0024] In a possible implementation manner of the first aspect, determining a dynamic motion model of a three-axis MEMS gyroscope based on uncertainty factors includes:

[0025] Based on the uncertainty factors, uncertain parameters are formed;

[0026] Based on the dimensionless motion model and uncertain parameters of the three-axis MEMS gyroscope, the dynamic motion model of the three-axis MEMS gyroscope is determined; the dynamic motion model of the three-axis MEMS gyroscope has preset boundary conditions.

[0027] In a possible implementation of the first aspect, determining a Lyapunov function based on an expected trajectory tracking error and a parameter estimation error of a dynamic motion model of a three-axis MEMS gyroscope includes:

[0028] Determine the sliding surface based on the trajectory tracking error of the dynamic motion model of the three-axis MEMS gyroscope;

[0029] Calculate the first-order derivative of the sliding membrane surface and determine the control law of the sliding membrane surface to deal with uncertain factors;

[0030] Based on the first-order derivative of the synovial surface and the control law, the parameter estimation error is determined, and the simplified first-order derivative of the synovial surface is obtained; the simplified first-order derivative of the synovial surface includes the parameter estimation error and the desired trajectory tracking error;

[0031] Based on the parameter estimation error and the desired trajectory tracking error in the first-order derivative of the simplified sliding membrane surface, the Lyapunov function is determined.

[0032] In a possible implementation of the first aspect, the Lyapunov function It is expressed as:

[0033]

[0034] Where s is the expected trajectory tracking error of the three-axis MEMS gyroscope, s T is the transpose of s; is the parameter estimation error, for is the transpose of ; Γ is the symmetric positive definite matrix of adaptive adjustment.

[0035] In a possible implementation manner of the first aspect, a sliding condition of the adaptive sliding film control of the three-axis MEMS gyroscope is expressed as:

[0036]

[0037] in, is the first-order derivative of the Lyapunov function; s is the expected trajectory tracking error of the three-axis MEMS gyroscope; ||s|| is the norm of s; η is the ideal positive value condition.

[0038] In a second aspect, the present application provides a controller, which is used to execute the adaptive control method for orthogonal error compensation as in the first aspect.

[0039] In a third aspect, the present application provides an adaptive control system for orthogonal error compensation, comprising a controller as in the second aspect and a three-axis MEMS gyroscope.

[0040] It can be understood that the beneficial effects of the second to third aspects mentioned above can be found in the relevant description of the first aspect mentioned above, and will not be repeated here.

[0041] Compared with the prior art, the embodiments of the present invention have the following beneficial effects:

[0042] In the embodiment of the present application, compared with the dual-axis gyroscope, the three-axis gyroscope has a more complex influence between the axes due to the increase in the number of axes, and more factors that cause errors. The compensation method needs to consider the comprehensive influence of the coupling damping and coupling stiffness coefficients between the three axes, so a compensation algorithm suitable for the three-axis MEMS gyroscope is proposed. By obtaining the coupling damping and coupling stiffness of the three-axis MEMS gyroscope, these key parameters directly reflect the dynamic characteristics of the internal structure of the gyroscope and the influence of the orthogonal error on the gyroscope. The motion model established based on these parameters can more accurately simulate the actual working state of the gyroscope; at the same time, by changing to a dimensionless motion model, the dimension effect is eliminated and the mechanism study is facilitated, and then by designing the sliding conditions of the adaptive sliding film control, the orthogonal error is directly compensated. The adaptive control algorithm is combined with the sliding film control to effectively compensate for the orthogonal error and improve the output accuracy of the three-axis MEMS gyroscope.

[0043] It is to be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the present specification. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0045] Figure 1 is a flow chart of an adaptive control method for orthogonal error compensation provided by an embodiment of the present application;

[0046] Figure 2 It is a schematic diagram of a three-axis MEMS gyroscope motion model provided in an embodiment of the present application;

[0047] Figure 3 It is a schematic diagram of a process for forming a dimensionless motion model of a three-axis MEMS gyroscope provided in an embodiment of the present application;

[0048] Figure 4It is a schematic diagram of a flow chart of determining the sliding condition of the adaptive sliding film control of the three-axis MEMS gyroscope provided by an embodiment of the present application;

[0049] Figure 5 It is a schematic diagram of the structure of a controller provided in one embodiment of the present application. DETAILED DESCRIPTION

[0050] In the following description, specific details such as specific system structures, technologies, etc. are provided for the purpose of illustration rather than limitation, so as to provide a thorough understanding of the embodiments of the present application. However, it should be clear to those skilled in the art that the present application may also be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to prevent unnecessary details from obstructing the description of the present application.

[0051] It should be understood that when used in the present specification and the appended claims, the term "comprising" indicates the presence of described features, integers, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or combinations thereof.

[0052] It should also be understood that the term “and / or” used in the specification and appended claims refers to any and all possible combinations of one or more of the associated listed items, and includes these combinations.

[0053] As used in the specification and appended claims of this application, the term "if" can be interpreted as "when" or "uponce" or "in response to determining" or "in response to detecting", depending on the context. Similarly, the phrase "if it is determined" or "if [described condition or event] is detected" can be interpreted as meaning "uponce it is determined" or "in response to determining" or "uponce [described condition or event] is detected" or "in response to detecting [described condition or event]", depending on the context.

[0054] In addition, in the description of the present application specification and the appended claims, the terms "first", "second", "third", etc. are only used to distinguish the descriptions and cannot be understood as indicating or implying relative importance.

[0055] References to "one embodiment" or "some embodiments" etc. described in the specification of this application mean that one or more embodiments of the present application include specific features, structures or characteristics described in conjunction with the embodiment. Therefore, the statements "in one embodiment", "in some embodiments", "in some other embodiments", "in some other embodiments", etc. that appear in different places in this specification do not necessarily refer to the same embodiment, but mean "one or more but not all embodiments", unless otherwise specifically emphasized in other ways. The terms "including", "comprising", "having" and their variations all mean "including but not limited to", unless otherwise specifically emphasized in other ways.

[0056] The basic principle of MEMS gyroscope is to use Coriolis force to transfer energy. When the axis of rotation of the gyroscope is perpendicular to the direction of a force, it will feel the force, thus generating a torque to rotate the coordinate system.

[0057] The three-axis MEMS gyroscope can simultaneously measure the angular velocity in the three axes of X, Y, and Z, while ordinary MEMS gyroscopes can usually only measure the angular velocity in a single axis. This multi-axis measurement capability enables the three-axis MEMS gyroscope to provide more comprehensive and accurate angular velocity information in complex dynamic environments. Although the two-axis MEMS gyroscope can also measure the angular velocity in two axes, compared to the three-axis gyroscope, its angular velocity change in the third axis is unknown, which may be limited in some applications that require comprehensive attitude perception.

[0058] Because the three-axis MEMS gyroscope can measure the angular velocity in the three axes of X, Y, and Z at the same time, its error sources are more complicated. In addition to the scale factor error, zero bias error, and non-orthogonality error in each axis, it is also necessary to consider the cross-coupling error that may exist between the three axes. This cross-coupling error may cause the angular velocity change on one axis to affect the measurement on another axis, thereby increasing the difficulty of error compensation.

[0059] Due to the complexity of the error sources, the design and implementation of the compensation algorithm is more complicated. Not only the error in each axis needs to be considered, but also the cross-coupling error between axes and the mutual influence between different error sources.

[0060] In terms of control algorithms, two-axis MEMS gyroscopes focus more on the control of a single or a few degrees of freedom. For example, in applications such as drones or robots, two-axis gyroscopes may be used to control the rotational motion of the horizontal plane. Therefore, its control algorithm may be relatively simple, focusing more on improving stability and accuracy. The three-axis MEMS gyroscope requires higher adaptability in terms of control algorithms. Since it can measure the angular velocity in three axes at the same time, it can be applied to a wider range of three-dimensional space control scenarios. In the control algorithm, the mutual influence and coupling relationship between the three axes need to be fully considered to achieve a more precise and complex control strategy.

[0061] Therefore, taking into account that the orthogonal error caused by the inevitable processing errors in the manufacturing process is an important factor affecting the accuracy of the three-axis MEMS gyroscope, the inventor proposed an adaptive sliding film control algorithm for orthogonal error compensation of the three-axis MEMS gyroscope, which effectively reduces the impact of external interference and parameter changes on the output accuracy of the gyroscope. Since the sliding film control is insensitive to parameter changes, the adaptive method is combined with the sliding film control to improve the algorithm stability and effectively realize orthogonal error compensation.

[0062] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0063] Figure 1 is a flow chart of an adaptive control method for orthogonal error compensation provided by an embodiment of the present application, with reference to Figure 1 , the adaptive control method for quadrature error compensation is described as follows:

[0064] The embodiment of the present application provides an adaptive control method for orthogonal error compensation, which is applied to a three-axis MEMS gyroscope. The method includes:

[0065] Step 101, obtaining coupling damping and coupling stiffness of a three-axis MEMS gyroscope.

[0066] Exemplarily, the coupling damping and coupling stiffness of the three-axis MEMS gyroscope are tested on a turntable, and the coupling damping and coupling stiffness are the effects of the orthogonal error.

[0067] At the same time, the control force, angular velocity, displacement, and equivalent damping d of the mass block of the three-axis MEMS gyroscope in the three axes of x, y, and z can be obtained. xx ,d yy ,d zz , equivalent stiffness k xx ,k yy ,k zz Motion parameters such as Figure 2 shown.

[0068] Step 102: forming a dimensionless motion model of the three-axis MEMS gyroscope based on the coupling damping and coupling stiffness of the three-axis MEMS gyroscope.

[0069] Exemplarily, in order to remove the influence of dimension on the law described by the three-axis MEMS gyroscope and facilitate further mechanism research, the initial motion model of the three-axis MEMS gyroscope is obtained after considering the coupling damping and coupling stiffness. It obtains the dimensionless motion model of the three-axis MEMS gyroscope by dimensionlessly processing the initial motion model.

[0070] Step 103 : determining the sliding condition of the adaptive sliding film control of the three-axis MEMS gyroscope based on the dimensionless motion model of the three-axis MEMS gyroscope.

[0071] Exemplarily, an adaptive sliding mode control algorithm is designed for the dimensionless motion model of the three-axis MEMS gyroscope, such as determining the sliding mode surface, the control law, defining the corresponding Lyapunov function, and determining the final adaptive law, so as to determine the sliding conditions, which can ensure that the trajectory of the three-axis MEMS gyroscope reaches the sliding membrane surface within a limited time and stays on the sliding membrane surface in the form of vibration.

[0072] Step 104 : Control the three-axis MEMS gyroscope based on the sliding condition of the adaptive sliding film control.

[0073] Exemplarily, under the sliding condition of the adaptive sliding film control, the evaluation parameters can be further made to converge to their actual values, and the orthogonal error converges to zero, thereby achieving orthogonal error compensation for the three-axis MEMS gyroscope.

[0074] In this embodiment, compared with the dual-axis gyroscope, the three-axis gyroscope has a more complex influence between the axes due to the increase in the number of axes, and more factors that cause errors. The compensation method needs to consider the comprehensive influence of the coupling damping and coupling stiffness coefficients between the three axes, so a compensation algorithm suitable for the three-axis MEMS gyroscope is proposed. By obtaining the coupling damping and coupling stiffness of the three-axis MEMS gyroscope, these key parameters directly reflect the dynamic characteristics of the internal structure of the gyroscope and the influence of the orthogonal error on the gyroscope. The motion model established based on these parameters can more accurately simulate the actual working state of the gyroscope; at the same time, by changing to a dimensionless motion model, the dimension effect is eliminated and the mechanism study is facilitated. Then, by designing the sliding conditions of the adaptive sliding film control, the orthogonal error is directly compensated. The adaptive control algorithm is combined with the sliding film control to effectively compensate for the orthogonal error and improve the output accuracy of the three-axis MEMS gyroscope.

[0075] In one embodiment, a specific implementation method for forming a dimensionless motion model of a three-axis MEMS gyroscope is introduced. Figure 3 , step 102 comprises:

[0076] Step 1021 , using the coupling damping and coupling stiffness of the three-axis MEMS gyroscope, an initial motion model of the three-axis MEMS gyroscope is formed.

[0077] For example, the initial motion model of a vibrating three-axis MEMS gyroscope can be expressed as:

[0078]

[0079] Among them, F x , F y , F z are the control forces in the three axes of x, y, and z respectively; m is the mass of the mass block; Ω x ,Ω y ,Ω y are the angular rates input around the x, y, and z axes respectively; x, y, and z are the displacements along the x, y, and z axes respectively, is the first-order derivative of displacement x with respect to time, is the second-order derivative of displacement x with respect to time; is the first-order derivative of displacement y with respect to time, is the second-order derivative of displacement y with respect to time; is the first-order derivative of the displacement z with respect to time, is the second-order derivative of displacement z with respect to time; d xx ,d yy ,d zz are the equivalent damping in the three axes of x, y and z; k xx ,k yy ,k zz are the equivalent stiffness in the three axes of x, y and z respectively; d xy =d yx is the coupling damping between the x-axis and the y-axis, d xz =d zx is the coupling damping between the x-axis and the z-axis, d tz =d zy is the coupling damping between the y-axis and the z-axis; k xy =k yx is the coupling stiffness between the x-axis and the y-axis, k xz =k zx is the coupling stiffness between the x-axis and the z-axis, k yz =k zy is the coupling stiffness between the y-axis and the z-axis. The coupling damping and coupling stiffness reflect the influence of the orthogonal error.

[0080] Step 1022 , performing dimensionless processing on the initial motion model of the three-axis MEMS gyroscope to obtain a dimensionless motion model of the three-axis MEMS gyroscope.

[0081] Exemplarily, first define the matrix according to the above three-axis MEMS gyroscope initial motion model:

[0082] Displacement Matrix Damping Matrix Stiffness Matrix Angular rate matrix and control matrix

[0083] Therefore, the initial motion model of the three-axis MEMS gyroscope can be expressed as:

[0084]

[0085] in, is the first-order derivative of the displacement matrix q′ in the x, y, and z axes, is the second-order derivative of the displacement matrix q′ in the x, y, z axes; D′ is the damping matrix; the elements of the damping matrix include equivalent damping and coupling damping; K′ is the stiffness matrix; the elements of the stiffness matrix include equivalent stiffness and coupling stiffness; u′ is the control force matrix in the x, y, z axes; Ω′ is the angular velocity matrix.

[0086] Define dimensionless time t, dimensionless damping D, dimensionless stiffness K and dimensionless angular velocity Ω: t = ω0t′, ω0 is the frequency of the oscillator in the resonant state. Substituting the dimensionless time t, dimensionless damping D, dimensionless stiffness K and dimensionless angular velocity Ω into formula (2), the dimensionless motion model of the three-axis MEMS gyroscope is obtained:

[0087]

[0088] in, is the first-order derivative of the dimensionless displacement matrix q in the x, y, and z axes, is the second-order derivative of the displacement matrix q in the x, y, z axes; D is the dimensionless damping matrix; the elements of the damping matrix include equivalent damping and coupling damping; K is the dimensionless stiffness matrix; the elements of the stiffness matrix include equivalent stiffness and coupling stiffness; u is the dimensionless control force matrix in the x, y, z axes; Ω is the dimensionless angular velocity matrix.

[0089] In this embodiment, based on the obtained motion parameters of the mass block of the three-axis MEMS gyroscope in the three axes of x, y, and z, such as control force, angular velocity, displacement, equivalent damping, equivalent stiffness, coupling damping, and coupling stiffness, a dynamic equation of the initial motion model of the vibrating three-axis MEMS gyroscope that takes into account the mutual coupling effects of the three axes is formed, which is conducive to analyzing the influence of orthogonal errors, and then by changing it to a dimensionless motion model, the dimensional influence is eliminated and subsequent mechanism research is facilitated.

[0090] In one embodiment, a specific implementation method for determining the sliding condition of the adaptive sliding film control of the three-axis MEMS gyroscope is introduced. Figure 4 , step 103 comprises:

[0091] Step 1031, obtaining uncertainty factors of the dimensionless motion model of the three-axis MEMS gyroscope.

[0092] Exemplarily, the uncertainty factors may include external disturbance terms, uncertainty of the dimensionless damping matrix, and uncertainty of the dimensionless stiffness matrix.

[0093] Step 1032: Determine the dynamic motion model of the three-axis MEMS gyroscope based on the uncertainty factors.

[0094] Exemplarily, step 1032 includes:

[0095] Based on the uncertainty factors, uncertain parameters are formed. For example, all uncertainties are gathered together to form the uncertain parameter l un .

[0096] Based on the dimensionless motion model and uncertain parameters of the three-axis MEMS gyroscope, the dynamic motion model of the three-axis MEMS gyroscope is determined.

[0097] Using the uncertain parameter l un Describing the dynamic changes of the dimensionless motion model of the three-axis MEMS gyroscope, the dynamic motion model of the three-axis MEMS gyroscope is expressed as:

[0098]

[0099] Where d is the external disturbance term, ΔD represents the uncertainty of the dimensionless damping matrix D, and ΔK represents the uncertainty of the dimensionless stiffness matrix K.

[0100] The dynamic motion model of the three-axis MEMS gyroscope has preset boundary conditions. The preset boundary conditions can be expressed using the norms of each component as:

[0101]

[0102] By defining reasonable boundary conditions, reasonable range limits are set for the system's dynamic behavior, ensuring that under specific operating conditions, the system's state variables will not exceed physical limits or safety ranges. This can reduce the uncertainty range of the model's prediction results, help to more accurately predict the system's response under different input conditions, and provide a reliable basis for the design and optimization of control algorithms.

[0103] Step 1033 , determining a Lyapunov function based on the expected trajectory tracking error and parameter estimation error of the dynamic motion model of the three-axis MEMS gyroscope.

[0104] Exemplarily, step 1033 includes:

[0105] First, the sliding surface is determined based on the trajectory tracking error of the dynamic motion model of the three-axis MEMS gyroscope. The sliding surface can be expressed as:

[0106]

[0107] Where e is the tracking error, e = qq m ,q m is the reference position, λ is a fixed positive definite matrix; s(t) is the function of the expected trajectory tracking error with respect to time.

[0108] Next, the first-order derivative of the sliding membrane surface is calculated, and the control law of the sliding membrane surface is determined to cope with the uncertainty factors.

[0109] The derivative of the synovial surface with respect to time is calculated according to formula (4) and formula (6). The first-order derivative of the synovial surface is expressed as:

[0110]

[0111] Where, u is the control input; ω1, ω2, ω3 are known driving frequencies; W is the regression matrix; p is the unknown vector of parameters. W and p are specifically defined as:

[0112]

[0113] p=[d xx d xy d xz d yx d yy d yz d zx d zy d zz Ω x Ω y Ω z n xx n xy n xz n yx n yy n yz n zx n zy n zz ] (9)

[0114] Based on the first-order derivative of the synovial surface and the control law, the parameter estimation error is determined, and the simplified first-order derivative of the synovial surface is obtained; the simplified first-order derivative of the synovial surface includes the parameter estimation error and the desired trajectory tracking error.

[0115] To make is 0, the equivalent control input u of the control input u eq It can be expressed as:

[0116]

[0117] To cope with external disturbances and uncertainties, the control law is set as:

[0118]

[0119] in, is the parameter estimate of parameter p; u lun = -Hsgn(s), H = diag(η1,η2,η3), sgn(s) is the sign function of the expected trajectory tracking error s.

[0120] Combining formulas (7) and (11), we can Simplified to:

[0121]

[0122] in, is the vector of parameter estimation errors;

[0123] Then, the Lyapunov function is determined based on the parameter estimation error and the desired trajectory tracking error in the first-order derivative of the simplified sliding membrane surface.

[0124] Considering the parameter estimation error and trajectory tracking error, in order to stabilize the entire system and make the expected trajectory tracking error s zero, the Lyapunov function It is expressed as:

[0125]

[0126] Where s is the expected trajectory tracking error of the three-axis MEMS gyroscope, s T is the transpose of s; is the parameter estimation error, for is the transpose of ; Γ is the symmetric positive definite matrix of adaptive adjustment; the superscript T in each symbol indicates the transpose.

[0127] Step 1034: Determine an adaptive law for adaptive sliding film control of the three-axis MEMS gyroscope based on the Lyapunov function.

[0128] Formula (13) is the derivative of the Lyapunov function with respect to time, and combined with formula (12), we can get The first derivative of

[0129]

[0130] in, is the parameter estimation error The first derivative of ; i = 1, 2 and 3.

[0131] To make If it is a negative number, the scalar unsigned item can be set to 0, that is, Then the adaptive law is expressed as:

[0132]

[0133] Step 1035 : determining a sliding condition of the adaptive sliding film control of the three-axis MEMS gyroscope based on an adaptive law of the adaptive sliding film control of the three-axis MEMS gyroscope.

[0134] When the parameter p changes, Combining formula (14) and formula (15), and assuming that η′=η1=η2=η3 is an ideal positive value, let η=η′-‖l un ‖≥0, the sliding condition of the adaptive sliding film control of the three-axis MEMS gyroscope is expressed as:

[0135]

[0136] in, is the first-order derivative of the Lyapunov function; s is the expected trajectory tracking error of the three-axis MEMS gyroscope; ||s|| is the norm of s; η is the ideal positive value condition.

[0137] The above sliding conditions can ensure that the trajectory reaches the sliding surface within a limited time and stays on the sliding surface in the form of tremors. is semi-negative definite (i.e., for all non-equilibrium states, the derivative is less than or equal to 0, and is strictly less than 0 at the non-equilibrium point for at least a certain period of time), and the expected trajectory tracking error s and parameter estimation error It is bounded. Further deduction and use of Barabalat's lemma show that the evaluation parameters can converge to their actual values, which proves that the system is asymptotically stable, thus achieving orthogonal error compensation for the three-axis MEMS gyroscope.

[0138] It can be seen that the adaptive control method for orthogonal error compensation of the three-axis MEMS gyroscope proposed in the present invention, combined with the adaptive method and the sliding film control, can effectively compensate for the orthogonal error and improve the output accuracy of the three-axis MEMS gyroscope.

[0139] And considering that compared with the dual-axis gyroscope, the three-axis gyroscope has more axes and more complex influences between axes, and more factors that cause errors, the compensation method needs to consider the comprehensive influence of the coupling damping and coupling stiffness coefficients between the three axes. Therefore, a compensation algorithm suitable for the three-axis MEMS gyroscope is proposed. By obtaining the coupling damping and coupling stiffness of the three-axis MEMS gyroscope, these key parameters directly reflect the dynamic characteristics of the internal structure of the gyroscope and the influence of orthogonal errors on the gyroscope. The motion model established based on these parameters can more accurately simulate the actual working state of the gyroscope; at the same time, by changing to a dimensionless motion model, the dimension effect is eliminated and the mechanism study is convenient.

[0140] See also Figure 5 , one embodiment provides a controller, which is used to execute the adaptive control method of orthogonal error compensation in the above embodiment.

[0141] The present application also provides a controller, see Figure 5 The controller 200 may include: at least one processor 210 and a memory 220, wherein the memory 220 stores a computer program that can be run on at least one processor 210, and when the processor 210 executes the computer program, the steps in any of the above method embodiments are implemented.

[0142] Exemplarily, the computer program may be divided into one or more modules / units, one or more modules / units are stored in the memory 220, and executed by the processor 210 to complete the present application. One or more modules / units may be a series of computer program segments capable of completing specific functions, and the program segments are used to describe the execution process of the computer program in the controller 200.

[0143] Those skilled in the art will understand that Figure 5 These are merely examples of controllers and do not constitute a limitation of the controller, which may include more or fewer components than those shown in the figure, or a combination of certain components, or different components, such as input and output devices, network access devices, buses, etc.

[0144] The processor 210 may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor, etc.

[0145] The memory 220 may be an internal storage unit of the controller or an external storage device of the controller, such as a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, etc. The memory 220 is used to store computer programs and other programs and data required by the controller. The memory 220 may also be used to temporarily store data that has been output or is to be output.

[0146] The bus may be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. The bus may be divided into an address bus, a data bus, a control bus, etc. For ease of representation, the bus in the drawings of the present application is not limited to only one bus or one type of bus.

[0147] The rapid intelligent detection method for physical and chemical indicators of hazardous waste provided in the embodiments of the present application can be applied to controllers such as computers, tablet computers, laptops, netbooks, personal digital assistants (PDAs), etc. The embodiments of the present application do not impose any restrictions on the specific type of controller.

[0148] An embodiment provides an adaptive control system for orthogonal error compensation, including the above controller and a three-axis MEMS gyroscope.

[0149] The system controls the output of the three-axis MEMS gyroscope through an adaptive control method of orthogonal error compensation set by a controller.

[0150] It should be understood that the size of the serial numbers of the steps in the above embodiments does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present application.

[0151] The beneficial effects of a manufacturing method refer to the beneficial effects of the smoking device self-cleaning method of the above embodiment.

[0152] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. An adaptive control method for orthogonal error compensation, characterized in that: Applied to a three-axis MEMS gyroscope, the method comprises: Obtaining coupling damping and coupling stiffness of the three-axis MEMS gyroscope; Based on the coupling damping and coupling stiffness of the three-axis MEMS gyroscope, a dimensionless motion model of the three-axis MEMS gyroscope is formed; Determining a sliding condition of an adaptive sliding film control of the three-axis MEMS gyroscope based on a dimensionless motion model of the three-axis MEMS gyroscope; The three-axis MEMS gyroscope is controlled based on the sliding condition of the adaptive sliding film control.

2. The adaptive control method for quadrature error compensation according to claim 1, characterized in that: The dimensionless motion model of the three-axis MEMS gyroscope is formed based on the coupling damping and coupling stiffness of the three-axis MEMS gyroscope, including: The coupling damping and coupling stiffness of the three-axis MEMS gyroscope are used to form an initial motion model of the three-axis MEMS gyroscope; the coupling damping and coupling stiffness reflect the influence of orthogonal error; The initial motion model of the three-axis MEMS gyroscope is dimensionally processed to obtain a dimensionless motion model of the three-axis MEMS gyroscope.

3. The adaptive control method for quadrature error compensation according to claim 1, characterized in that: The dimensionless motion model of the three-axis MEMS gyroscope is expressed as: in, is the first-order derivative of the dimensionless displacement matrix q in the x, y, and z axes, is the second-order derivative of the dimensionless displacement matrix q in the x, y, z axes; D is the dimensionless damping matrix; the elements of the dimensionless damping matrix include equivalent damping and coupling damping; K is the dimensionless stiffness matrix; the elements of the dimensionless stiffness matrix include equivalent stiffness and coupling stiffness; u is the dimensionless control force matrix in the x, y, z axes; Ω is the dimensionless angular velocity matrix.

4. The adaptive control method for quadrature error compensation according to claim 1, characterized in that: The step of determining the sliding condition of the adaptive sliding film control of the three-axis MEMS gyroscope based on the dimensionless motion model of the three-axis MEMS gyroscope comprises: Obtaining uncertainty factors of a dimensionless motion model of the three-axis MEMS gyroscope; Based on the uncertainty factors, determining a dynamic motion model of the three-axis MEMS gyroscope; Determining a Lyapunov function based on a desired trajectory tracking error and a parameter estimation error of a dynamic motion model of the three-axis MEMS gyroscope; Based on the Lyapunov function, determining an adaptive law of the adaptive sliding film control of the three-axis MEMS gyroscope; Based on an adaptive law of the adaptive sliding film control of the three-axis MEMS gyroscope, a sliding condition of the adaptive sliding film control of the three-axis MEMS gyroscope is determined.

5. The adaptive control method for quadrature error compensation according to claim 4, characterized in that: The step of determining the dynamic motion model of the three-axis MEMS gyroscope based on the uncertainty factor includes: Based on the uncertainty factors, forming uncertain parameters; Based on the dimensionless motion model of the three-axis MEMS gyroscope and the uncertain parameters, a dynamic motion model of the three-axis MEMS gyroscope is determined; the dynamic motion model of the three-axis MEMS gyroscope has preset boundary conditions.

6. The adaptive control method for quadrature error compensation according to claim 4, characterized in that: The method of determining a Lyapunov function based on an expected trajectory tracking error and a parameter estimation error of a dynamic motion model of the three-axis MEMS gyroscope comprises: Determining a sliding membrane surface based on a trajectory tracking error of a dynamic motion model of the three-axis MEMS gyroscope; Calculating the first-order derivative of the sliding membrane surface and determining a control law of the sliding membrane surface to cope with the uncertainty factor; Based on the first-order derivative of the synovial surface and the control law, a parameter estimation error is determined, and a simplified first-order derivative of the synovial surface is obtained; the simplified first-order derivative of the synovial surface includes the parameter estimation error and a desired trajectory tracking error; A Lyapunov function is determined based on the parameter estimation error and the desired trajectory tracking error in the simplified first-order derivative of the synovial surface.

7. The adaptive control method for quadrature error compensation according to claim 4, characterized in that: The Lyapunov function It is expressed as: Where s is the expected trajectory tracking error of the three-axis MEMS gyroscope, s T is the transpose of s; is the parameter estimation error, for is the transpose of ; Γ is the symmetric positive definite matrix of adaptive adjustment.

8. The adaptive control method for quadrature error compensation according to any one of claims 1 to 7, characterized in that: The sliding condition of the adaptive sliding film control of the three-axis MEMS gyroscope is expressed as: in, is the first-order derivative of the Lyapunov function; s is the expected trajectory tracking error of the three-axis MEMS gyroscope; ||s|| is the norm of s; η is the ideal positive value condition.

9. A controller, characterized in that: The controller is used to execute the adaptive control method for orthogonal error compensation as described in any one of claims 1-7.

10. An adaptive control system for orthogonal error compensation, characterized in that: It comprises the controller as claimed in claim 9 and a three-axis MEMS gyroscope.

Images